Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - 5.3 Fundamental Theorem of Calculus - 5.3 Exercises: 32

Answer

\[\sqrt 2 \]

Work Step by Step

\[\begin{gathered} \int_0^{\pi /4} {2\cos x} dx \hfill \\ \hfill \\ {\text{Integrate using }}\int {\cos x} dx = \sin x + C \hfill \\ \hfill \\ 2\left[ {\sin x} \right]_0^{\pi /4} \hfill \\ \hfill \\ {\text{Fundamental Theorem of calculus}} \hfill \\ \hfill \\ 2\left[ {\sin \left( {\frac{\pi }{4}} \right) - \sin \left( 0 \right)} \right] \hfill \\ \hfill \\ {\text{Simplify and subtract}} \hfill \\ \hfill \\ 2\left[ {\frac{{\sqrt 2 }}{2}} \right] \hfill \\ \hfill \\ \sqrt 2 \hfill \\ \end{gathered} \]
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